1. Data Cube Computation Model dependencies among the aggregates: most detailed “view” can be computed from view (product,store,quarter) by summing-up all quarterly sales product,store,quarter productstorequarter none store,quarterproduct,quarterproduct, store

2. Computation Directives Hash/sort based methods (Agrawal et. al. VLDB’96) 1.Smallest-parent 2.Cache-results 3.Amortize-scans 4.Share-sorts 5.Share-partitions product,store,quarter productstorequarter none store,quarterproduct,quarterproduct, store

3. Alternative Array-based Approach Model data as a sparse multidimensional array – partition array into chunks (a small sub-cube which fits in memory). – fast addressing based on (chunk_id, offset) Compute aggregates in “multi-way” by visiting cube cells in the order which minimizes the # of times to visit each cell, and reduces memory access and storage cost. B What is the best traversing order to do multi-way aggregation?

4. Roadmap What is the data warehouse, data mart Multi-dimensional data modeling Data warehouse design – the star schema, bitmap indexes The Data Cube operator – semantics and computation Aggregate View Selection

5. Views and Decision Support OLAP queries are typically aggregate queries. – Pre-computation is essential for interactive response times. – The CUBE is in fact a collection of aggregate queries, and pre-computation is especially important: lots of work on what is best to pre-compute given a limited amount of space to store pre-computed results. Warehouses can be thought of as a collection of asynchronously replicated tables and periodically maintained views. – Has renewed interest in view maintenance!

6. Materialized Views A view whose tuples are stored in the database is said to be materialized. – Provides fast access, like a (very high-level) cache. – Need to maintain the view as the underlying tables change. – Ideally, we want incremental view maintenance algorithms. Close relationship to data warehousing, OLAP, (asynchronously) maintaining distributed databases, checking integrity constraints, and evaluating rules and triggers.

7. Issues in View Materialization Algorithm to maintain a materialized view? What views should we materialize, and what indexes should we build on the pre- computed results? Given a query and a set of materialized views (possibly with some indexes), can we use the materialized views to answer the query?

8. View Selection Problem Use some notion of benefit per view Limit: disk space product,store,quarter productstorequarter none store,quarterproduct,quarterproduct, store Hanarayan et al SIGMOD’96: Pick views greedily until space is filled

9. Reality check:too many views! 2 n views for n dimensions (no- hierarchies) Storage/update- time explosion More pre- computation doesn’t mean better performance!!!!

10. Sources of Information - Books 1.The Data Warehouse Toolkit – Ralph Kimball ISBN 0- 471-15337-0 2.The Data Warehouse Lifecycle Toolkit – Ralph Kimball, Laura Reeves, Warren Thornthwaite & Margy Ross ISBN 0-471-25547-5 3.Data Warehouse Design Solutions – Christopher Adamson & Michael Venerable ISBN 0-471-25195-X

11. Sources of Information – Web Sites Technology Guides for Data Warehousing - www.techguide.comwww.techguide.com Ralph Kimball Associates Articles - www.ralphkimball.com/html/articles.htmlwww.ralphkimball.com/html/articles.html Data Warehousing - Data Warehousing Knowledge Center - www.datawarehousing.orgwww.datawarehousing.org The Data Warehousing Information Center - www.dwinfocenter.orgwww.dwinfocenter.org Documenting data replication and data transformation sites on the Net - www.datawarehousing.comwww.datawarehousing.com DM Review Business Intelligence & Data Warehousing Enabling E-Business - www.dmreview.com/www.dmreview.com/ The Data Warehousing Institute - www.dw-institute.comwww.dw-institute.com Intelligent Enterprise Magazine - www.intelligententerprise.com/www.intelligententerprise.com/ DataWarehousing Forum - www.datawarehousing.com/forum/www.datawarehousing.com/forum/